Sizhuk A. Microscopic dynamic theory and kinetics for model system of the non-polar molecules

Thesis is devoted to the investigation of the model system of the non-polar molecules taking into account internal degrees. The model of the hard spherical molecules has been considered. The mechanical energy symmetry to action of the reflection operator of the state vector is considered. For the model mechanism of the momentum and angular momentum exchange between the hard rough spheres an explicit mathematical expression of the reflection operator is found. For the particles with the rough surface a mechanism for the moment-of-momentum exchange is proposed and a kinetic equation for the one-particle probability density is derived. The model mechanism of the momentum and angular momentum exchange between the hard rough spheres corresponds with hard particles: the modulus in torsion and the modulus in tension is infinite large (the shear deformation and the torsional strain is absent). In the case of a mirror hyperplane reflection of state vector in the collisions, it is proved that evolution equation for microscopic density in the nine-dimensional phase space can be presented in the form of the Boltzmann-Enskog's Equation.. The evolution equation for the microscopic phase density of model dynamical system taking into account border conditions has been constructed. The interaction with the surface has been described by reflection operator. The evolution equation for microscopic density can be used for approximate equations building of the averaged microscopic density. This approximate equation for the macroscopic distribution (the averaged microscopic density) can be used for study of kinetics and hydrodynamics of respective statistical system taking into account interaction with a plane surface. Thus, in the case of mirror reflection operator obtained Enskog-like evolution equation for macroscopic density in the nine-dimensional phase space has the microscopic solution, which can be presented by delta-distribution. As an example using the exact equation it was built approximation, which describes system kinetics near the equilibrium position. For the system in the case of the spatially homogeneous one-particle probability density the kinetic equation was studied.. It has been obtained analytic expression for temperature as time function near equilibrium state in case of local equilibrium and nonequilibrum Maxwell's distribution on degrees of freedom. It was shown that the relaxation time is inversely proportional to the distribution and to the second root of equilibrium temperature. It was shown that the relaxation time has minimal value for moment of inertia, which equals shell moment of inertia with effective radius. From expressions for relaxation time it was obtained that relation of the relaxation time of the system of rough spheres to relaxation time of the system of rough shells equals 1.176.